What distribution do you get from this broken random shuffle?

The famous Fisher-Yates shuffle algorithm can be used to randomly permute an array A of length N:

For k = 1 to N
    Pick a random integer j from k to N
    Swap A[k] and A[j]

A common mistake that I've been told over and over again not to make is this:

For k = 1 to N
    Pick a random integer j from 1 to N
    Swap A[k] and A[j]

That is, instead of picking a random integer from k to N, you pick a random integer from 1 to N.

What happens if you make this mistake? I know that the resulting permutation isn't uniformly distributed, but I don't know what guarantees there are on what the resulting distribution will be. In particular, does anyone have an expression for the probability distributions over the final positions of the elements?